Modern Higher Algebra
Abraham Adrian Albert (1905-72) was an American mathematician primarily known for his groundbreaking work on algebra. In this book, which was originally published in 1938, Albert provides a detailed exposition of 'modern abstract algebra', taking into account numerous discoveries in the field during the preceding ten years. A glossary is included. This is a highly informative book that will be of value to anyone with an interest in the development of algebra and the history of mathematics.
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RINGS WITH A UNITY ELEMENT
SYMMETRIC AND SKEw MATRICES
THE GALOIs THEORY
The degree of a total matric algebra
The cyclic representation of a total matric algebra
The polynomial algebra A
ALGEBRAs OF MATRICES
abelian group additive abelian group archimedean ordered assume called characteristic function commutative complex numbers composition series contains correspondence cosets cyclic field cyclic group cyclic of degree defined derived field determinant diag diagonal elements divides divisible division ring divisorless ideal divisors of zero elementary transformations equivalence relation evidently EXERCISES exists an integer Hence implies independent indeterminates integral domain invariant factors irreducible ith row LEMMA linear combinations linear set linearly independent matrices with elements minimum function monic polynomial multiplication n-rowed square matrices non-singular non-singular matrix non-trivial null sequence number field obtain ordered field p-adic number permutation proof properties prove Theorem quadratic quantities rank rational numbers real numbers regular sequence relatively prime replace result ring 21 root field scalar Show solvable square matrix stem fields subfield subgroup subring subset T-equivalent T-symmetric theory tion total matric algebra u.f. domain unique unit unity element valuation write